The present invention relates to computerized systems and methods for exploration of and learning about effects that emerge from interrelations between basic elements of complex systems. More particularly, the invention relates to systems and methods which generate representations of interactions between elements created, selected, and transformed by a user for purposes of learning.
Computers have provided opportunities for significant advances in educational processes. They have been increasingly used in teaching, particularly for young children who have become extremely adept at using computers. Much educational software is based upon a teacher or tutor model, in which the system guides the user in specific areas with predefined objectives and information to be learned. Such systems interpret different levels of achievement and assume that if the information given is below the user""s level, the user may become bored; if the information is above the user""s level, the user may become frustrated. Also, under a strict teaching approach, the user has no control over what is being learned. Points of interest to a specific user may be missed. Often instructional software, while presenting important information, is not particularly enjoyable to use; nor is the user""s resulting understanding particularly memorable. Therefore, a need exists for learning environments that permit a user to learn material at his or her own pace, exploring to depths of interest, and which are entertaining.
Complex, dynamic systems can be difficult to understand. Such systems do not operate according to a single set of rules that can be easily learned. Instead, they operate as dynamic networks of interdependent elements, which vary in unique ways based upon a large variety of factors present at a given point in time. The world is made up of great numbers of such systems, in both biological and physical domains. Examples of such systems are population growth, weather patterns, economic fluctuations, biological evolution, organizational behavior, and traffic patterns. Since it is difficult to describe such complex systems, not many tools are available for exploring and learning about them. Therefore, a need exists for a system which provides opportunities for learning about and understanding how these complex processes operate.
Mathematics, particularly the mathematics of geometry and spatial relationships, provides opportunities for studying complex systems in ways that can be made simple, enjoyable, and understandable. One way for people, particularly children, to develop mathematical and spatial skills is by working with patterns. Thus, educators and parents encourage children to play with toys that use and manipulate patterns, such as tilings, kaleidoscopes, moire patterns, quilts, mosaics, tangrams, and geometric puzzles. The use of such playthings permits a child to learn by increasing his or her spatial skills while engaged in entertaining activities. However, many existing toys minimize control by the user, limit constructive capabilities that are useful for learning, do not allow for lengthy, rigorous explorations, and cannot capture the dynamic aspects of complex systems.
The deficiencies of prior educational tools are substantially overcome by the computer-based systems and methods of present invention, which represent interrelated dynamics of complex systems. The system uses the advantage of the memory and computational capacity of computers to allow a user to learn about complex systems through constructive exploration and play. The invention may be implemented as a playful learning environment in which people, particularly children, experiment with dynamic systems by constructing and transforming virtual objects through dialogic interaction with a computational device. The user creates or selects basic elements of the system having defined characteristics. In an embodiment involving geometric patterns, the user begins with a simple design. In embodiments involving sociodynamic systems, the user works with physical or behavioral patterns. The system then operates on the basic elements, simulating and making visible the emergent effects of a complex system.
According to one aspect of the invention, the user can manipulate different aspects of the system, including changes in the basic elements or interactions. The user can also create new basic elements from the interactions within the complex environment. Alternatively, the system may impose operations programmatically to illustrate alternate dynamic qualities of the complex system.
According to another aspect of the invention, methods and apparatus are provided for constructive-dialogic learning. A computational system provides elements for constructing objects. The system also provides a user mode having user functions for application to the elements and a system mode having system functions for application to the elements. In response to user selection of one of the elements and the user mode, a user function is applied to the selected element under user control. In response to user selection of one of the elements and the system mode, a system function is applied to the selected element under system control. Thus, operation of the system involves a combination of user control and system control. This combination is dialogic in nature. The user constructs an object from the elements utilizing the user functions and the system functions through user-controlled, constructive, dialogic interaction with the system.
According to a further aspect of the invention, methods and apparatus are provided for learning in a learning environment including a learner tool, a partner tool, objects, and operations. The method of the invention includes selecting a degree of control over the the learner tool, the partner, the objects, and a subset of the operations, wherein the subset of operations is associated with the selected degree of control, selecting a subset of the objects and interacting with the learner tool and the partner tool to manipulate the subset of objects with the subset of operations according to the selected degree of control. The interaction enables a constructive dialogue between a user and the learning environment.
The selected degree of control over the learner tool and the partner tool is within a range of total learner tool control and total partner tool control. The selected degree of control may be shared between the learner tool and the partner tool to promote turn taking between the learner tool and the partner tool while interacting.
In embodiments of the invention, the objects may comprise geometric patterns, such as tiles, or animated figures, such as creatures. Operations may include, for example, creating objects, modifying objects, saving objects in a library, and replicating objects. The learner tool may include a learner interface and the partner tool may include a partner interface. The sizes of the learner interface and the partner interface may be varied according to the selected degree of control. Learner operations may include generating objects having specified characteristics under user control, and partner operations may include causing the generated objects to interact in accordance with the specified characteristics.